Multiple choice

What is the length of the perpendicular drawn from the centre of circle of radius $r$ on the chord of length $\sqrt {3}r$?

  1. $r$
  2. $\sqrt {2}r$
  3. $r/2$
  4. $r/4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distance from the center to a chord of length L is sqrt(r^2 - (L/2)^2). Here L = sqrt(3)r. Distance = sqrt(r^2 - (sqrt(3)r/2)^2) = sqrt(r^2 - 3r^2/4) = sqrt(r^2/4) = r/2.

AI explanation

The perpendicular from the centre to a chord bisects the chord, creating a right triangle where the hypotenuse is the radius r and the base is half the chord length, which is sqrt(3)r divided by 2. Using the Pythagorean theorem, the perpendicular length squared equals r squared minus (sqrt(3)r divided by 2) squared, yielding r squared minus 3r squared divided by 4, which equals r squared divided by 4. Taking the square root gives the perpendicular length as r/2.

Keep practicing — related questions